Prove that the determinent |{:(x,sinthet...

Prove that the determinent `|{:(x,sintheta,costheta),(-sintheta,-x,1),(costheta,1,x):}|` is independent from value of `theta`

Text Solution

Verified by Experts

The correct Answer is:

`-x^3`

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Prove that, (2costheta+1)(2costheta-1) (2cos2theta-1)(2cos4theta-1)=2cos8theta+1

If sintheta+costheta=1 , then find the general value of theta .

Knowledge Check

Let A=[{:(1,sintheta,1),(-sintheta,1,sintheta),(-1,-sintheta,1):}] where 0lethetalepi then

A

det(A)

B

`det(A)in(2,oo)`

C

`det(A)in(2,4)`

D

`det(A)in[2,4]`

The solution set of sintheta+costheta=2 is ………

A

`kpi,kinZ`

B

`2kpi+(pi)/(2),kinZ`

C

`phi`

D

`(2k+1)(pi)/(2),kinZ`

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If 21 tan theta= 20 , show that (1-sintheta+costheta)/(1+sintheta+costheta)=3/7

If sectheta=13/5 , show that (2sintheta-3costheta)/(4sintheta-9costheta)=3

Prove the following identities : (sintheta-costheta+1)/(sintheta+costheta-1)=1/(sectheta-tantheta)

The value of the determinant {:|(alpha,beta,l), (alpha,x, n),(alpha,beta,x)|:} is a. independent of l b. independent of n c. alpha(x-l)(x-beta) d. alphabeta(x-l)(x-n)

Simplify costheta[(costheta,sin theta),(-sintheta,costheta)]+sin[(sintheta,-costheta),(costheta,sintheta)]

Evaluate the determinants below in examples number 1 and 2 |{:(costheta,-sintheta),(sintheta,costheta):}|

KUMAR PRAKASHAN-DETERMINANTS -MISCELLANEOUS EXERCISE - 4

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